Post date: Oct 31, 2015 11:47:54 PM
If f and g are convex, then
1)Â f+g is convex, and max(f, g) is convex. More generally, if f(x, y) is convex in x, then sup_y f(x, y) is convex in x.
2) f is non-decreasing, f(g) is convex. f is non-increasing, f(-g) is convex.
3) g(x) = Ax+b (affine), f(g) is convex